Chapter 5: Issues in Externality ControlPositive ExternalitiesPositive externalityAn Economic Model of Positive Externalities-1An Economic Model of Positive Externalities-2An Economic Model of Positive Externalities-3An Economic Model of Positive Externalities-4Positive v. Negative externalitiesPolluter Heterogeneity and Markets for PollutionTransferable permitMathematical expression-1Mathematical expression-2Mathematical expression-3Chapter 5: Issues in Externality ControlPositive ExternalitiesPolluter HeterogeneityThe Benefits of Pollution TradingProblems Associated with Pollution Permit MarketsChoice of Pollution Taxes or StandardsSpecification of Pollution in Productive ActivitiesComponents of Externality PolicyTechnology DiffusionPositive ExternalitiesA positive externality exists if activities of one agent leads to increases in the utility or productive ability of some other agents, and the benefits are not transmitted through a market. Inefficient outcome.Examples of positive externality:-Apple farmer and neighboring honey producer if the honey producer’s bees pollinate the apple trees. Unless the apple farmer pays the bee keeper for the marginal value of pollinating services, the bee keeper will not recognize this value in her objective function and thus keep an inefficiently low number of bees.Positive externalityQ*= optimal outputP*c=optimal consumer priceP*p= (P*c + S*) = optimal producer priceQc= competitive outputPc= competitive priceS*=subsidy= P*p - P*c = MEB = optimal subsidy [note that S*=MEB(Q*)]An Economic Model of Positive Externalities-1Ex. Fertilizer manufacturers uses animal waste as an input and generates a positive externality by removing the waste from the environment. Let: X= the amount of animal waste used by fertilizer manufacturers. D(P) = the fertilizer manufacturers’ demand for XPB(X) = the fertilizer manufacturers’ private benefit from output X EB(X) = environmental benefit of removed waste X.SB(X) = social benefit of X = PB(X) + EB(X).C(X) = cost of obtaining X.SW(X) = social welfare of using X = PB(X) + EB(X) - C(X)An Economic Model of Positive Externalities-2Market for Animal WasteSocial optimization problem:First-Order Condition:PBx +EBx - Cx = 0, or,MPB + MEB = MC.Hence, the socially optimal solution is to use X*animal waste, such that: MSB(X*) = MC(X*) Max SW X PB X EB X C XX. ( ) ( ) ( ) ( )  An Economic Model of Positive Externalities-3Quantity of fertilizer used is lower with externality than it is under socially optimal solution ( Qc < Q*). A subsidy S* = MEB(X*) will achieve the optimal solution.An Economic Model of Positive Externalities-4With subsidy S*, welfare implications are:Consumer gain = Pc*Pc BC Producers gain =AB PcPp* Environmental gain =MBCA Subsidy cost = Pc*CAPp* Net social gain =BAM.Positive v. Negative externalitiesAsymmetry between optimal policies for positive and negative externalities: 1) The likely policy to address positive externalities is a subsidy. 2) The likely policy to address negative externality is direct controls or taxes.Polluter Heterogeneity and Markets for PollutionWhen firms are heterogeneous and differ in their ability to abate their pollution, it is necessary to determine both the efficient amount of total emissions and the efficient mix of pollution among alternative sources. This may require that all polluting firms in a given location abate pollution to the same level, or perhaps that only one of many firms should abate.Transferable permitThe market approach, or transferable permit system to correct negative externalities attempts to establish markets for pollution.The approach uses economic incentives found in conventional markets to allocate pollution abatement between firms in the most cost-effective manner.Mathematical expression-1Assume there are I groups of polluters emitting pollution into a common medium. Assume also that all pollution is the same in the model and cannot be decomposed by location. Let: Xi= pollution generated by polluter i.Bi(Xi) =monetary benefit of polluter i derived from pollution.Total pollution = X = X1 + X2 + X3, . . ., XI SC(X) = social cost of pollution.Social optimization problem is: Max ,subject to Using Lagrange multiplier techniques, this problem becomeswhere, , the shadow price of pollution = marginal cost to society from an added unit of pollution. Xii 1IB (X ) SC( )ii 1IiXii 1Imax L B (X ) SC( ) Xii 1Ii ii 1I    Mathematical expression-2Social optimization problem: FOC: where, marginal benefit of polluter i from polluting and = MSC = marginal social cost of pollution. max L B (X ) SC( ) Xii 1Ii ii 1I    LXiLXiBiXi0 for i 1,ILL SC0    BiXiBXiiMBiSCSCMathematical expression-3At the optimal solution, MBi = MSC =  for all i. Marginal benefit of pollution is equal across producers and equal to marginal cost of pollution. The optimal solution can be attained by a unit tax, t*=MSC(X *), which could be charged for each unit of pollution.The optimal solution can also be attained by trading pollution permits, where total pollution is restricted to the optimal pollution level, X*. At the optimal solution, assuming competitive trading, the price of a pollution permit will be